form_element(7) bilinear form on a single element

SYNOPSYS

The form_element class defines functions that compute a bilinear form defined between two polynomial basis on a single geometrical element. This bilinear form is represented by a matrix.

The bilinear form is designated by a string, e.g. "mass", "grad_grad", ... indicating the form. The form depends also of the geometrical element: triangle, square, tetrahedron (see geo_element(2)).

IMPLEMENTATION NOTE

The form_element class is managed by (see smart_pointer(2)). This class uses a pointer on a pure virtual class form_element_rep while the effective code refers to the specific concrete derived classes: mass, grad_grad, etc.

IMPLEMENTATION

```template <class T, class M>
class form_element : public smart_pointer<form_element_rep<T,M> > {
public:
// typedefs:
typedef form_element_rep<T,M>         rep;
typedef smart_pointer<rep>            base;
typedef typename rep::size_type       size_type;
typedef typename rep::vertex_type     vertex_type;
typedef typename rep::space_type      space_type;
typedef typename rep::geo_type        geo_type;
typedef typename rep::coordinate_type coordinate_type;
// constructors:
form_element ();
form_element (
std::string           name,
const space_type&     X,
const space_type&     Y,
const geo_type&       omega,
// accessors & modifier:
void operator() (const geo_element& K, ublas::matrix<T>& m) const;
virtual bool is_symmetric () const;
// for scalar-weighted forms:
void set_weight (const field_basic<T,M>& wh) const;
bool is_weighted() const;
const field_basic<T,M>& get_weight () const;
// for banded level set method:
bool is_on_band() const;
const band_basic<T,M>& get_band() const;
void set_band (const band_basic<T,M>& bh) const;
};

```